# Simplifying Quadratic Equations Worksheets

The main purpose of working with quadratic equations is to find the value of the missing variable. In the standard form of the equation that value is most likely represented by x. There are a number of different ways in which you can solve for that value. We often work with the quadratic equation formula to solve them. When it is possible to use that formula, it is usually the easiest. If your starting point does not fit into the formula, you can always look to simplify that starting equation. The most common way to simplify is by dividing out the common factors before you attempt to solve it. Even if it does not allow you to apply it to the formula as a result, you will be left with easier numbers to work with. These worksheets and lessons will have you practice manipulate quadratic equations and help you become accustom to simplifying them.

### Aligned Standard: HSN-CN.C.7

- Find x Step-by-step Lesson- Find the two forms of x from a quadratic equation.
- Guided Lesson - Solve three quadratics for us.
- Guided Lesson Explanation - I provide a universal version of the quadratic formula and then we work away on using it.
- Practice Worksheet - I line up ten quadratics for you to pick apart and find me an x value.
- Matching Worksheet - Match the quadratics to the possible value of their x.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Working with quadratics in straight format.

- Homework 1 - Most of these are solving by factoring.
- Homework 2 - Remeber to factor in the same fashion.
- Homework 3 - Start all of these by moving all terms to one side of the equals symbol.

### Practice Worksheets

These are all followed with detailed explanations. This should help it click faster.

- Practice 1 - Solve all the quadratic equations.
- Practice 2 - In most cases you will use addition or subtraction of terms in the first step.
- Practice 3 - After everything is to one side, factor it to the end.

### Math Skill Quizzes

I would definitely have some scrap paper available for these quizzes.

- Quiz 1 - Your thrid step should be to make the factor value equal to zero.
- Quiz 2 - Then list the solutions to the original.
- Quiz 3 - Solve this bad boy: X
^{2}+ 24x + 140 = -4

### How to Simplify Quadratic Equations

We all have studied quadratic equations quite a few times. They are the equations that contain a variable that is actively being squared, in most cases it presents as x^{2}. A quadratic equation is used in many complex problems to simplify them. The standard way of writing a quadratic equation can be written as: ax^{2} + bx + c, where a = 0. The unknown variable (x) is the only value that is not known in the equation. Because of the nature of this type of equation the value of a cannot be zero.

To simplify a quadratic equation, there are three methods to follow: factoring method, the quadratic formula method, and completing the square method.

**Factoring** - Leaving the zero on one side, take all the terms on one side. Now factor them. Set each factor to zero and solve each of these equations. Now make sure that the equation is satisfied by putting the answer in the original equation to confirm your values.

**The Quadratic Formula** - Another method of solving quadratic equations involves the use of the following formula. This is where you use the equation:

x = (-b ± √ - 4ac / 2a)

Since variables a, b, and c are known just plug those values in. Remember that the presence of ± symbol will result in two answers.

**Completing the Square** - Convert the equation in the form; ax^{2} + bx = - c.

Ensure that a = 1 (if not, multiply the equation by 1/a before proceeding). With the value of b derived from the new equation, add (b/2)^{2} to both sides of the equation and make it a perfect square. Now you can make square roots of both sides of the equation.